What Is the Identity Function in Math?

By Staff WriterLast Updated Mar 29, 2020 12:48:27 AM ET

The identity function in math is one in which the output of the function is equal to its input, often written as f(x) = x for all x. The input-output pair made up of x and y are always identical, thus the name identity function. This holds true not only for the set of all real numbers, but also for the set of all real functions. Often considered mathematically trivial, the identity function is the basis for all other functions.